A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is:

Explanation

Consider the forces acting on the ball as shown in the figure.

`T cos theta` component will cancel mg.
`T sin theta` component will provide necessary cnetripetal force to the ball towards centre C.
`thereforeTsintheta=mromega^(2)=m(lsintheta)omega^(2)" or "T=mlomega^(2)`
`therefore"Angular velocity "omega=sqrt((T)/(ml))`
or `omega_("max")=sqrt((T_("max"))/(ml))=sqrt((324)/(0.5xx0.5))=36rads^(-1)`